Method for adjusting a resistance-gage force transducer and an adjusted force transducer thus obtained

ABSTRACT

A force transducer comprises a resilient bar (1) which carries a measuring bridge formed by resistance gages (R 1 , . . . R 4 ). One end of the bar is attached to a stationary support (2) and the other end is subjected to a force (P) to be measured. A method for ensuring that the signal delivered by the measuring bridge is proportional to the applied force and insensitive to parasitic couples consists in determining the initial characteristics of the transducer, in computing the relative errors arising from a displacement of the force (P) applied as a function of the angle made between the resistance gages (R 1 , . . . R 4 ) and the longitudinal direction (O x ) of the bar (1) and in cancelling these errors by making changes in one or a number of gages in order to modify the angle aforesaid.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method for adjusting a resistance-gage force transducer.

The invention is also directed to a resistance-gage force transducer which is adjusted in particular by means of the method aforesaid.

2. Description of the Prior Art

Transducers of the above-mentioned type are already known in which one end of a resilient metal bar is attached to a stationary support and the other end is subjected to the force to be measured. This force is usually applied to a plate which is parallel to the bar and connected to this latter at the end remote from the stationary support.

The fixed bar carries resistance-type strain gages which are electrically connected to each other and form a measuring bridge for delivering an electrical signal which is a function of the force applied to the plate aforesaid.

Depending on the point of application of force on the plate, said force gives rise to variable torsional and flexural couples which act on the bar to modify the value of the electrical signal delivered by the measuring bridge and thus impair the accuracy of measurement of this force.

In consequence, appropriate steps should be taken to make this measurement insensitive to the parasitic couples just mentioned, thereby ensuring that the signal delivered is constant irrespective of the point of application of the force on the plate.

Two methods are at present in use for ensuring insensitivity of measurement of force with respect to the parasitic couples aforesaid.

In a first method, the plate rests on a system of levers which summates the forces applied to the plate and transmits the resultant force on a predetermined point to the measuring device.

In a second method, the plate is attached directly to a transducer which is often of highly complex shape so designed as to minimize the effect of the parasitic couples or moments. The transducer is usually adjusted by means of mechanical actions in order to eliminate residual effects of the parasitic moments.

In the method described in French patent No. 82 20040, an attempt has been made to solve the difficulties noted in the foregoing by eliminating the parasitic torsion signal generated at the time of application of force on the plate by means of one or a number of torsion strain gages and additional resistors of suitable design which are inserted in the signal-processing circuit.

However, this method does not permit elimination of the parasitic signal which is related to the displacement of the point of application of the force in a direction parallel to the axis of the resilient bar.

SUMMARY OF THE INVENTION

The aim of the present invention is to provide a method for adjusting the force transducer in such a manner as to ensure that the electrical measurement signal is insensitive to the torsional and flexural couples generated by displacements of the point of application of the force to be measured, said method being simple to carry out and readily adaptable to automatic operation.

In accordance with the invention, said method is distinguished by the following steps:

A. Determination of the initial characteristics of the transducer.

B. Computation of the relative errors of the transducer arising from a displacement of the applied force as a function of the angle θ formed between the resistance gages and the longitudinal direction of the bar.

C. Cancellation of these errors by making modifications in one or a number of resistance gages in order to produce a modification of the above-mentioned angle θ.

The present Applicant has in fact found that it was possible to compute the relative errors of the transducer arising from displacements of the applied force as a function of the angle θ formed between the resistance gages and the resilient bar.

It is consequently possible to cancel these errors by making modifications in one or a plurality of resistance gages, the effect thereby achieved being to modify the angle θ aforesaid.

The method in accordance with the invention thus calls for a single sequence of operations involving solely a modification of the angle θ formed by one or a number of resistance strain gages, with the result that the force transducer delivers a signal which remains strictly proportional to the force to be measured, irrespective of the point of application of this force relatively to the bar.

In view of the fact that the method produces a modification in only one parameter of the resistance gages, this method is readily automatable or adaptable to automatic operation.

It has been established by the present Applicant that the errors of the transducer are a function of the angle θ aforesaid in accordance with the following relations:

    e.sub.x =e.sub.x.sbsb.o +1/C.sub.x  Σ  cos 2θ

    e.sub.z =e.sub.z.sbsb.o +1/C.sub.z  Σ  sin 2θ

where

e_(x) and e_(z) are the errors due to a displacement of the force (P) applied respectively along an axis O_(x) of the bar and along an axis O_(z) perpendicular to said bar axis and to the applied force P,

e_(x).sbsb.o and e_(z).sbsb.o are the initial errors determined during the step which involves initial characterization of the transducer,

C_(x) and C_(z) are known constants which are established by design and by the conditions of initial characterization of the transducer.

By means of these relations, it is therefore possible to compute the correction to be made in the angle θ for cancelling the aforementioned errors e_(x) and e_(z).

It is then only necessary to develop an industrial and automatable method for making this correction of the angle θ in the resistance gages.

According to another aspect of the invention, the resistance-gage force transducer provided by the invention and comprising a resilient bar such that one end of said bar is intended to be attached to a stationary support and the other end is subjected to the force to be measured, said bar being adapted to carry resistance gages electrically connected to each other so as to form a measuring bridge for delivering an electrical signal which is a function of the force applied to said end of the bar, said transducer being so adjusted as to ensure that the signal is proportional to the applied force while being insensitive to the torsional and flexural couples generated by the displacements of the point of application of the force to be measured, is distinguished by the fact that the angle θ formed between one and a plurality of resistance gages and the longitudinal direction of the bar satisfies the following relations:

    e.sub.x =e.sub.x.sbsb.o +1/C.sub.x  Σ  cos 2θ=0

    e.sub.z =e.sub.z.sbsb.o +1/C.sub.z  Σ  sin 2θ=0

where

e_(x) and e_(z) are the errors due to a displacement of the force applied respectively along the axis O_(x) of the bar and along an axis O_(z) perpendicular to said axis and to the applied force,

e_(x).sbsb.o and e_(z).sbsb.o are the initial errors determined during a step which involves initial characterization of the transducer,

C_(x) and C_(z) are known constants established by design and by the conditions of said initial characterization.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features of the invention will be more apparent upon consideration of the following description and accompanying drawings, wherein:

FIG. 1 is a view in perspective showing a force transducer in accordance with the invention, said transducer being attached to a stationary support;

FIG. 2 is a diagram showing the measuring bridge formed by the resistance strain gages of the transducer;

FIG. 3 is a schematic side view of the force transducer to which is attached a plate for application of the force to be measured;

FIG. 4 is a schematic end view of the force transducer and of the plate;

FIG. 5 is a plan view of a resistance strain gage which has been modified in accordance with one of the embodiments of the method provided by the invention;

FIG. 6 is a view which is similar to FIG. 5 and relates to another embodiment of the method;

FIG. 7 is a plan view of four resistance strain gages each comprising a principal resistor and two additional resistors in series and forming an angle with the principal resistor;

FIG. 8 is a view which is similar to FIG. 7 and relates to another example of construction.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 illustrates a resilient bar 1 of constant rectangular cross-section which is attached to a stationary support 2. The end of said bar 1 remote from the support 2 is subjected to a force P to be measured, said force being perpendicular to the axis O_(x) of said bar.

Four resistance strain gages R₁, R₂, R₃, R₄ are placed on said bar 1 and connected electrically to each other so as to form a measuring bridge (as shown in FIG. 2) which is supplied with a voltage V_(A) and delivers an output signal V_(S).

It has been found by experience that the ratio of the output signal to the supply signal of a transducer of this type is of the form:

    V.sub.S /V.sub.A =AP[a+bX+cZ]+z

In this relation, the terms PX and PZ are the parasitic flexural and torsional couples produced by the position of the force P on a plate 3 which extends in a direction parallel to the bar 1 and is attached to that end of this latter which is remote from the stationary support 2 (as shown in FIGS. 3 and 4).

The letter z is a constant term defining the unbalance of the measuring bridge when no applied force is present.

The parasitic signals APbX and APcZ have a large number of different causes which can be grouped together under the following main headings:

metallurgical heterogeneity within the bar 1 or within the gages R₁ . . . R₄,

errors in position-location of the gages,

parasitic resistances in the measuring bridge,

finite dimensions of the bar 1.

The many different causes of error reduce any prospect of obtaining a perfect transducer directly, that is to say a transducer in which b and c are zero and in which, in addition, z is equal to 0 or has a specified value.

The principle which forms the basis of the method in accordance with the invention will first be described.

Consider by way of example a thin resistor of length L, of width l and of thickness t bonded by its surface L.1 to a deformable substrate such as a resilient bar. The variation in value of resistance of this resistor is: ##EQU1##

Moreover, the variation in resistivity Δρ/ρ is related to the variation in volume of the resistor ΔV/V by the Bridgman relation: ##EQU2## whence ##EQU3##

Since the resistor is very thin and bonded to the substrate, ΔL/L and Δ1/1 are imposed by the deformation of the substrate; these deformations give rise to stresses σ_(L) and σ_(l) in the resistor. On the other hand, the external surface of the resistor is free to move, and we have σt=0.

Hooke's law in the resistor permits evaluation of Δt/t, by means of the following relations: ##EQU4##

The first two relations yield: ##EQU5##

The third: ##EQU6## νR=Poisson constant of the resistor. Thus: ##EQU7##

Now if the length L of the resistor makes an angle θ with the principal direction O_(x) of the bar, the state of plane deformation of which is specified by its three components: ε_(x) ε_(z) γ_(xz), the conventional formulae give the deformations: ΔL/L and Δ1/1 in the resistor, and we find: ##EQU8##

In consequence: ##EQU9##

By virtue of conventional considerations in regard to strength of materials, the surface deformations εx εz γxz at the abscissa x of the bar 1 (see FIGS. 3 and 4) can be expressed as a function of the forces applied to its free end: transverse load P, bending moment P(X-L), torsional moment PZ, we have:

    εx=Py/EI(X-x)

    εz=-μPv/EI(X-x)

    γ=Pv/C·Z

wherein:

EI: flexural rigidity of bar 1

C: torsional rigidity of bar 1

2 v: thickness of bar 1

L: length of bar 1

μ: Poisson constant of bar 1

hence:

εx+εz=AP(1-μ)(X-x)

εx-εz=AP(1+μ)(X-x)

γ=AP·BZ

(A=v/EI and B=EI/C characterize the bar 1).

Surface deformations may be expressed in a more detailed manner. The simple expressions given above, however, suffice to gain an understanding of the method.

The variation in value of a resistor which is bonded to the loaded bar 1 then becomes: ##EQU10## is the longitudinal gage coefficient usually considered in extensometry; it is equal to 2 when the Bridgman coefficient ##EQU11## is equal to 1, which is approximately the case with many of the usual alloys.

The expression given in the foregoing applies to isotropic piezoresistive materials characterized by C>1.

The signal of a bridge constituted by four resistors having equal ohmic values R₁, R₂, R₃, R₄ and bonded to the bar (A,B) is: ##EQU12##

Considering the odd-numbered disconnected resistors R₁, R₃ having as abscissa -Δ and the even-numbered resistors R₂, R₄ +Δ as indicated in FIG. 1, the signal is:

    S=AP/4[4GΔ+(1+μ)ΔΣ(cos 2θ-1)+(1+μ)X Σ cos 2θ+BZ Σ  sin 2θ]

in this expression and in those which will be employed hereinafter:

Σ (a) represents the sum a₁ +a₂ +a₃ +a₄

Σ (a) represents the sum in the bridge:

    a.sub.1-a.sub.2 +a.sub.3 -a.sub.4.

If all the angles θ are zero, the signal S is reduced to

    AP/4 4GΔ

The portion of the signal related to the angles θ is:

    Sθ=AP/4[(1+μ)ΔΣ(cos 2θ-1)+(1+μ)x Σ  cos 2θ+BZ Σ  sin 2θ]

By superimposing the influence of the angles θ, isolated in the foregoing, on the signal of a real transducer which, as shown by experience, is of the form:

    AP/4[a+bX+cZ]+z

a≅4GΔ

bX<<a error related to the position X of P

cZ<<a error related to the position Z of P

z zero error of the bridge

we obtain:

    S=AP/4[4GΔ+(1+μ)ΔΣ(cos 2θ-1)+(b+(1+μ) Σ  cos 2θ)X+(c+B Σ  sin 2θ)Z]+z+Δz

    S=AP/4[4GΔ+(1+μ)ΔΣ(cos 2θ-1)+(b+(1+μ) Σ  cos 2θ)X+(C+B Σ  sin 2θ)Z]+z+Δz

This expression shows that modifications of the angles θ in resistors of suitable parity make it possible to cancel the coefficients of X and of Z at the cost of a small signal loss (1+μ)ΔΣ(cos 2θ-1) and of a variation in the zero Δz (which can in any case be compensated as will be seen later). Said expression constitutes the basis of the method which will now be described.

Although the initial angles θ can in principle be of any value, it is clearly advantageous to choose angles of zero value in order to ensure an initially zero signal loss (1+μ)ΔΣ(cos 2θ-1).

The method is not directly concerned with the origin of the initial errors b, c, z: it merely notes their existence and cancels them in a single operational sequence involving the following steps:

initial characterization of the transducer,

adjustment of resistances of the strain-gage bridge,

final checking of the transducer.

At the end of this sequence, the transducer is an integrated quadrupole component which ensures the function S=kP (k=constant) within specified tolerance limits. At the time of initial characterization of the transducer, the initial errors of this latter are determined by subjecting the bar to predetermined forces applied successively to the plate or like device at two points which are symmetrical with respect to the center of the strain-gage bridge in the longitudinal axis of the bar and at two points which are also symmetrical with respect to the aforesaid center and located on an axis perpendicular to the longitudinal axis aforesaid.

The relative error arising from an eccentric displacement X of P on the plate 3 along the axis Ox is: ##EQU13##

The relative error arising from an eccentric displacement Z of P on the plate 3 along the axis Oz is: ##EQU14## Adjustment of the transducer consists: in cancelling ex: Σ cos 2θ=-C_(x) e_(x).sbsb.o

in cancelling ez: Σ sin 2θ=-C_(z) e_(z).sbsb.o

in cancelling or adjusting to the desired value the zero: z+Δz.

The initial errors ex_(O) and ez_(O) are known by means of the initial characterization of the transducer. Cx and Cz are known and established by design (G, Δ, B, μ) and by the conditions of characterization (X, Z).

The practical application of the principle of adjustment stated in the foregoing must ensure independence of the adjustments:

     Σ  cos 2θ=-Cxex.sub.o and  Σ  sin 2θ=-Czez.sub.o

and

must make provision for industrial means with a view to varying the angles θ. These two considerations will hereinafter be dealt with successively.

The two following methods are proposed for ensuring independence of adjustments.

FIRST METHOD

Starting from zero angles θ, if an angle dθ is formed on a resistor R₁, R₂, R₃ or R₄ and the values of sin 2dθ and cos 2dθ are modified simultaneously, ez and ex vary simultaneously, which usually precludes any possibility of obtaining ex=ez=0.

Independence of the adjustments ex=0 and ez=0 is ensured by partitioning each adjustment so that one-half is applied to a resistor modified by the angle +dθ and not to another resistor modified by the angle -dθ.

In the case of the adjustment ex=0, the modified resistors have the same parity.

In the case of the adjustment ez=0, the modified resistors have different parities.

Adjustment ex=0

Initial situation:

     Σ  cos 2θ=cos 0-cos 0+cos 0-cos 0=1-1+1-1

One-half of the error ex₀ is compensated by modifying a resistor by +dθ_(x) :

     Σ  cos 2θ=±(cos 2dθ.sub.x +1)∓(1+1)=±(cos 2dθ.sub.x -1)=-Cxex.sub.0 /2

The other half of ex₀ is compensated by modifying the resistor having the same parity by -dθ_(x).

     Σ  cos 2θ=±(cos 2dθ.sub.x +cos 2(-dθ.sub.x))∓(1+1)=±2(cos 2θ.sub.x -1)=-Cxex.sub.0

    e.sub.x =e.sub.x.sbsb.0 +1/Cx  Σ  cos 2θ=e.sub.x.sbsb.0 +1/Cx (-C.sub.x e.sub.x.sbsb.0)=0

The error e_(x) is cancelled and the consequential effect on e_(z) is zero:

    e.sub.z =e.sub.z.sbsb.0 +1/Cz[±(sin 2dθ.sub.x +sin 2(-dθ.sub.x))±(0+0)]=e.sub.z.sbsb.0

Adjustment e_(z) =0

Initially: Σ sin 2θ=0-0+0-0

First half: ±[sin 2dθ_(z) ]∓(0-0)=±sin 2dθ_(z) =-C_(z) e_(z).sbsb.0 /2

Second half: ±[sin 2dθ_(z) -sin 2(-dθ_(z))]∓(0-0)=±2 sin 2dθ_(z) =-C_(z) e_(z).sbsb.0

ez is now zero and the repercurssion on e_(x) =0 already achieved is also zero:

    1/Cx[±(cos 2dθ.sub.z -cos 2(-dθ.sub.z))]=0

the two adjustments can be performed in any order

choice of resistors to be adjusted (± signs in the expressions given above):

Adjustment e_(x) =0:

if e_(x0) >0,

Σ cos 2θ must be negative:

the odd-numbered resistors are therefore modified, cos 2dθ_(x) -1 is <0

if e_(x0) <0,

Σ cos 2θ must be positive:

the even-numbered resistors are modified: -(cos 2dθ_(x) -1) is >0.

Adjustment e_(z) =0:

if e_(z0) >0,

Σ sin 2θ must be negative:

an even-numbered resistor is modified by +dθ_(z) and an odd-numbered resistor is modified by -dθ_(z)

if e_(z0) <0,

Σ sin 2θ must be positive:

an odd-numbered resistor is modified by +dθ_(z) and an even-numbered resistor is modified by -dθ_(z).

Values of the angles dθ_(x) and dθ_(z) : ##EQU15##

Orders of magnitude:

with G=2 and X/Δ=Z/Δ=3, C_(x) ≅2, C_(z) ≅3 and e_(x0) =e_(z0) =0.03.

The method of partitioned adjustment described in the foregoing therefore entails the need to form angles:

    dθ.sub.x =(2.0.03/4).sup.1/2 =0.12 rad

    dθ.sub.z =3.0.03/4=0.02 rad

SECOND METHOD

If a systematic signal loss is found acceptable, it is possible to obtain virtual independence of adjustment without any need to partition these latter as mentioned earlier (each adjustment will be carried out on one resistor alone) by placing in each group having the same parity a resistor at θ=0 which is specialized in the adjustment e_(z) =0 and a resistor at θ=π/4 which is specialized in the adjustment e_(x) =0.

All the adjustments are then performed by the function sin 2(0+dθ) and all the repercussions are in cos 2(0+dθ).

Initial situation:

     Σ  cos 2θ=cos 0-cos 0+cos 2π/4-cos 2π/4=0

     Σ  sin 2θ=sin 0-sin 0+sin 2π/4-sin 2π/4=0

This configuration does not introduce any error e_(x) in e_(z).

Adjustment e_(x) =0 on the resistors at π/4:

A sign is chosen for dθ_(x) and there is then determined the parity of the resistor to be readjusted as a function of the sign of e_(x0) and of the sign chosen for dθ_(x) ; dθ_(x) is then formed on the suitable resistor:

     Σ  cos 2θ=1-1±cos 2(π/4+dθ.sub.x)=∓sin 2dθ.sub.x =-C.sub.x e.sub.x0 →dθ.sub.x ≅C.sub.x e.sub.x0 /2

the repercussion on e_(z) is very small:

    1/C.sub.z [0-0±sin 2(π/4+dθ.sub.x)∓sin 2(π/4)]=±1/C.sub.z (cos 2dθ.sub.x -1)=±(C.sub.x e.sub.x0).sup.2 /2C.sub.z

    e.sub.z0 becomes e.sub.z1 =e.sub.z0 ±(C.sub.x e.sub.x0).sup.2 /2C.sub.z

A measurement of e_(z1) is then performed and this latter is taken as a datum for the adjustment e_(z) =0.

Adjustment e_(z) =0 on the Resistors at 0°.

The parity and the sign of dθ_(z) are chosen as a function of e_(z1) and dθ_(z) is formed on the suitable resistor:

     Σ  sin 2θ=±(sin 2dθ.sub.z -0)∓(1-1)=sin 2dθ.sub.z =-C.sub.z e.sub.z1 →dθ.sub.z =C.sub.z e.sub.z1 /2

the repercussion on e_(x) =0 already adjusted is very small.

    1/C Σ  cos 2θ32 1/C.sub.x [±(cos 2dθ.sub.z -1)+cos π/2-cos π/2]=1/C.sub.x (cos 2dθ.sub.z -1)≅±(C.sub.z e.sub.z1).sup.2 /2C.sub.x

Since the order of magnitude of the repercussions is known at the time of initial characterization of the transducer, the program can be written in such a manner as to minimize the residual error. This method systematically produces a relative signal loss equal to: ##EQU16##

Value of the angles:

The adjustment e_(x) =0 results in formation of an angle dθ_(x) =C_(x) e_(x0) /2

The adjustment e_(z) =0 results in formation of an angle dθ_(z) =C_(z) e_(z1) /2

and leaves a maximum repercussion

namely (C_(x) e_(x0))² /2C_(z) on the error e_(x)

and ˜(C_(z) e_(Z0))² /2C_(x) on the error e_(z)

The order of adjustments can be chosen by programming so as to leave only the smaller of the two. This latter in any case tends towards zero after a second adjustment cycle.

After the corrections to be made in the angles θ have been determined by calculation and independence of the adjustments (e_(x) =e_(z) =0) has been ensured, either of the two methods described hereinafter is employed for the purpose of modifying the initial angles θ of the resistance strain gages.

The first method applies exclusively to thin-film or thick-film resistors.

This method consists in using a laser beam, for example, in order to cut a parallelogram in the initially rectangular resistance gages R₁, . . . R₄. As shown in FIG. 5, said parallelogram is defined by two parallel grooves l₁ and l₂, the electrical length L₁ of which really forms the angle dθ_(x) or dθ_(z) with respect to the initial orientation 0_(x), said angle being determined by the aforementioned expressions as a function of the initial characterization.

As shown in FIG. 6, it is also possible to form notches e₁, e₂ . . . in the longitudinal edges of the resistance gages R₁, . . . R₄, said notches being transverse to the direction 0_(x) or 0_(z) so as to ensure that the resultant electrical length L₁ forms with the initial direction 0_(x) or 0_(z) the angle dθ_(x) or dθ_(z) which is determined by the relations given earlier.

The maximum sensitivity of the error e_(x) or e_(z) to the variation of angle dθ_(x) or dθ_(z) is ##EQU17##

namely, as an order of magnitude, 1/2dθ

Checking of errors to within an accuracy of 0.001 therefore calls for angular checking which is accurate to 0.002 rad. Commercially available laser adjustment machines can readily attain this degree of accuracy.

With the orders of magnitude previously employed, the maximum variation of the zero produced by the adjustments e_(x) =0 and e_(z) =0 is

    |Δz|=1/42(L/1dθ)=0.06

(with L/1=1)

in the case of the method of partitioned adjustment.

    |Δz|=1/4L/1(dθ.sub.x +dθ.sub.z)=0.02

(with L/1=1)

in the case of the method of specialized resistors.

These variations are cancelled by conventional functional adjustment of a resistor having suitable parity along its transverse axis of symmetry in order to avoid modification of the angle.

The second method proposed consists in making use of resistance gages each formed by a principal resistor Ro which forms a predetermined angle with the longitudinal axis O_(x) of the bar 1. Each principal resistor Ro is connected to additional resistors, Ra, Rb, . . . , having a low ohmic value in comparison with that of the principal resistor Ro and forms a predetermined angle with the direction of the resistor Ro.

In order to cancel the errors e_(x) and e_(z), the ohmic value of one or a number of these additional resistors Ra, Rb is modified. The effect thereby achieved is to modify the virtual angle of the resistance gage with the axis 0_(x) of the bar 1.

This second method applies to all types of resistance gages (grids or layers) and is based on the following statement:

Considering a resistor formed by resistance elements in series R=R₀ +R₁ + . . . +R_(n), having the same abscissa x (in order to simplify the description which can in any case be transposed to parallel resistors):

R₀ forms the angle θ₀ with the longitudina axis of the bar 1 and R_(n) forms the angle θ_(n). ##EQU18##

With the aid of the formula established earlier:

    r.sub.i =AP[G(X-x)+(1+μ)(X-x)(cos 2θ.sub.i -1)+BZ sin 2θ.sub.i ],

we calculate:

    r=Σρ.sub.i r.sub.i =AP[G(X-x)Σρ.sub.i +(1+μ)(X-x)(Σρ.sub.i cos 2θ.sub.i -Σρ.sub.i)+BZΣρ.sub.i sin 2θ.sub.i ]

so that, by taking into account ##EQU19##

The sums of vectors Σρ_(i) cos 2θ_(i), Σρ_(i) sin 2θ_(i) are respectively proportional to ##EQU20## and perform the function of cos 2θ and sin 2θ in the formula of a single resistor.

The composite resistor R=R₀ +R₁ + . . . +R_(n) behaves as a single resistor having a virtual angle equal to: ##EQU21## A transducer equipped with resistors of this type can therefore be adjusted by modifying the virtual angles of these latter solely by conventional adjustment of the ratios of resistances ρ_(i).

Two examples of configuration are given below:

Example 1

As indicated in FIG. 7, each resistance strain gage of the bridge is formed by a principal resistor R₀ having a weight ρ which is close to 1 and forming a zero angle θ with 0_(x) so that sin 2θ=0 and cos 2θ=1, in series with a resistor R_(a) having a weight ρ'<<1 and forming an angle θ'=π/4 with 0_(x) so that: sin 2θ'=1, cos 2θ'=0 and with a resistor R_(b) having a weight ρ"=ρ'<<1 and forming an angle θ"=-π/4 with O_(x) so that sin 2θ"=-1, cos 2θ"=0. We calculate directly:

    Σρ.sub.i sin 2θ.sub.i =ρ×0+ρ'×1+ρ"×(-1)=ρ'-ρ"

    Σρ.sub.i cos 2θ.sub.i =ρ×1+ρ'×0+ρ"×0=ρ=1-(ρ'+ρ")

The initial virtual angle arctg ρ'-ρ"/ρ is zero if ρ'=ρ" in the case of each resistor.

Σ (1-ρ'-ρ")= Σ (ρ'-ρ") and Σ (ρ'-ρ") are also zero in a bridge made up of four identical resistors and this configuration does not in itself produce any error of the type e_(x) or e_(z). Should any differences exist between the different values ρ' and ρ", the resultant errors are counted in ex₀ and ez₀ during the initial measurement.

Adjustment of the transducer consists in increasing the ratios ρ' and ρ" by dρ' and dρ" in order to obtain:

     Σ (-dρ'-dρ")=-C.sub.x ex.sub.0

and thus to cancel ex

     Σ (dρ'-dρ")=-C.sub.z ez.sub.0

and thus to cancel ez.

The values dρ' and dρ" (which are necessarily positive) are employed both in ex and in ez.

As in the method of direct modification of the angles, independence of adjustments is ensured by distributing ("partitioning") them in two resistors (having the same parity in respect of ex=0 and having a different parity in respect of ez=0), one resistor being modified by dρ' and the other resistor being modified by dρ".

Adjustment ex=0:

    ±(dρ'.sub.x +dρ".sub.x)=-C.sub.x ex.sub.0 dρ'.sub.x =dρ".sub.x =C.sub.x |ex.sub.0 |/2

Repercussion on ez:

    ±1/C.sub.z (dρ'.sub.x -dρ".sub.x)=0

Adjustment ez=0:

    ±(dρ'.sub.z -(-dρ".sub.z))=-C.sub.z ez.sub.0 dρ'.sub.z =dρ".sub.z =C.sub.z |ez.sub.0 |/2

Repercussion on ex:

    ±1/C.sub.x (dρ'.sub.z -dρ".sub.z)=0

The sign of ex₀ determines the parity (±sign) of the adjusted group in order to produce ex=0.

The sign of ez₀ determines the combination (parity/angle) of the series resistor employed for producing ez=0.

In the method of direct subdivision of the angles explained earlier, it is possible to compute and to program the value of the angles dθ to be formed.

In the present method, the adjustment parameters are the ratios ρ' and ρ" which may not be accessible to measurement and may therefore not be programmable. In this case, the variations in these ratios dρ', dρ" are represented by the variations in the bridge zero which are always measurable.

The ratios ρ', ρ" have been defined by the series resistance/total resistance ratios, with the result that ##EQU22## Moreover, the variation in the bridge zero is: ##EQU23##

It is thus possible to program the values of dρ by means of variations of zero and to control the adjustments.

ex=0 produces a variation in zero=1/4(C_(x) ex₀ /2+C_(x) ex₀ /2) since two resistors having the same parity are adjusted.

ez=0 produces a variation in zero=1/4(C_(z) ex₀ /2-C_(z) ez₀ /2) since two resistors having a different parity are adjusted.

The uncertainty arising from the approximation ##EQU24## is removed if necessary by stopping the adjustment at 90% (for example) of the computed value, by making a new measurement of the errors and by computing a new modification of the zero.

After the adjustments ex=0 and ez=0, the zero (irrespective of its value) is brought to the specified value by a conventional functional adjustment of a principal resistor having a suitable parity.

Example II:

As indicated in FIG. 8, each resistance strain gage of the bridge is formed by a principal resistor R₀ having a weight ρ which is close to 1 and forming a zero angle θ with O_(x) so that sin 2θ=0, cos 2θ=1, in series with a resistor R_(a) having a weight ρ'<<1 and forming an angle θ'=π/4 with O_(x) so that sin 2θ'=1, cos 2θ'=0, with a resistor R_(b) having a weight ρ"=ρ' and forming an angle θ"=-π/4 with O_(x) and sin 2θ"=-1, cos 2θ"=0 and with a resistor R_(c) having a weight ρ"'<<1 and forming an angle θ"'=±π/2 with O_(x) so that sin 2θ"'=0, cos 2θ"'=-1.

We calculate directly: ##EQU25##

The initial virtual angle arctg (ρ'-ρ"/ρ-ρ"') is zero if ρ'=ρ" and a strain gage bridge constituted by four identical resistors of this type does not introduce any errors due to the configuration.

Adjustment of the transducer consists in setting: ##EQU26##

The resistors R_(c) at 90° having a weight ρ"' do not play any part in the adjustment e_(z) =0.

Independence of adjustments is therefore ensured if one adjusts in the following order: first of all e_(z) =0 by means of ρ' or ρ" (or both by partitioned adjustment), then e_(x) =0 by means of ρ"', then the zero on a principal resistor ρ.

The case of the method of partitioned adjustment will first be studied.

In the relations:

     Σ (dρ'-dρ")=(dρ'-dρ").sub.1 -(dρ'-dρ").sub.2 +(dρ'-dρ").sub.3 -(dρ'-dρ").sub.4

and

     Σ (-dρ'-dρ"-2dρ"')=(-dρ'-dρ"-2dρ"').sub.1 -(-dρ'-dρ"-2dρ"').sub.2

     +(-dρ'-dρ"-2dρ"').sub.3 -(-dρ'-dρ"-2dρ"').sub.4,

dρ'₁ and dρ'₃, dρ"₁ and dρ"₃, dρ'₂ and dρ'₄, dρ"₂ and dρ"₄, dρ"'₁ and dρ"'₃, dρ"'₂ and dρ"'₄ perform the same function. There is consequently no objection to dispensing with the series resistors R_(a), R_(b), R_(a1), R_(b1), R_(c3) and R_(c4) having respectively the weights ρ'₁, ρ"₁, ρ'₂, ρ"₂, ρ"'₃ and ρ"'₄, for example.

The adjustment values then become:

     Σ (dρ'-dρ")=(dρ'-dρ").sub.3 -(dρ'-dρ").sub.4 =(dρ'.sub.3 +dρ".sub.4)-(dρ".sub.3 +dρ'.sub.4)

     Σ (-dρ'-dρ"-2dρ"')=-2(dρ"'.sub.1 -dρ"'.sub.2)-(dρ'.sub.3 -dρ".sub.4)-(dρ".sub.3 -dρ'.sub.4)

The initial virtual angles of the four resistance gages of the bridge are zero. This configuration does not introduce in itself either an error of the type e_(x) or e_(z) or a signal loss.

The adjustment e_(z) =0 is obtained by:

     Σ (dρ'-dρ")=-C.sub.z ez.sub.0

by increasing ρ"₃ and ρ'₄ by the same quantity:

    dρ".sub.3 =dρ'.sub.4 =+C.sub.z ez.sub.0 /2,

if ez₀ >0

    dρ'.sub.3 =dρ".sub.4 =-C.sub.z ez.sub.0 /2,

if ez₀ <0

e_(x) has not varied:

    e.sub.x =e.sub.x0 +1/c.sub.x (C.sub.z e.sub.z0 /2-C.sub.z e.sub.z0 /2)=e.sub.x0

During the first half of the adjustment (dρ"₃), the zero varies approximately by:

    1/4 Σ dρ".sub.3 =C.sub.z e.sub.z0 /2.4

and, during the second half, by:

    1/4 Σ dρ'.sub.4 =-C.sub.z e.sub.z0 /2.4

These variations make it possible to program the adjustment with, if necessary, one or a number of intermediate measurements e_(z1) e_(z2) . . . .

After the adjustment e_(z) =0, the zero has reverted to its initial value.

The adjustment e_(x) =0 is then obtained by:

     Σ (-2dρ"')=-2(dρ"'.sub.1 -dρ"'.sub.2)=-C.sub.x e.sub.x0

ρ"'₁ is increased (if ex₀ >0) by dρ"'₁ =C_(x) e_(x0) /2

or ρ"'₂ is increased (if ex₀ <0) by dρ"'₂ =-C_(x) e_(x0) /2

During this adjustment, the zero varies approximately by:

    1/4 Σ dρ"'=1/4C.sub.x e.sub.x0 /2

The new zero is cancelled or brought to the desired value by conventional functional adjustment of a principal resistor (θ=0) having a parity determined by the sign of the new zero.

The configuration may be simplified even further and, instead of partitioning the adjustment e_(z) =0 as before, this adjustment may be performed on a single inclined resistor with, however, a greater zero correction at maximum value.

In the first of the adjustment values written earlier:

     Σ (dρ'-dρ")=(dρ'.sub.3 +dρ".sub.4)-(dρ".sub.3 +dρ'.sub.4)

     Σ (-dρ'-dρ"-2ρ"')=-2(dρ"'.sub.1 -dρ"'.sub.2)-(dρ'.sub.3 -dρ".sub.4)-(dρ".sub.3 -dρ'.sub.4)

it is possible to suppress one element within each pair of brackets (dρ"₃ and dρ"₄ for example) without reducing the capacity of adjustment e_(z) =0.

The adjustment equations become:

     Σ (dρ'-dρ")=dρ'.sub.3 -dρ'.sub.4 =-C.sub.z e.sub.z0

     Σ (-dρ'-dρ"-2dρ"')=-2(dρ"'.sub.1 -dρ"'.sub.2)-(dρ'.sub.3 -dρ'.sub.4)=-C.sub.x e.sub.x0

e_(z) =0 is obtained by increasing

ρ'₃ by -c_(z) e_(z0) if e_(z0) <0

or

ρ'₄ by C_(z) e_(z0) if e_(z0) >0

After this adjustment, e_(x) has become ex₁ =ex₀ +1/C_(x) C_(z) ez₀ and the zero has varied by ±1/4C_(z) e_(z0).

e_(x1) is measured (or calculated) and cancelled by: ##EQU27## by increasing ρ"'₁ by C_(x) e_(x1) /2 if ex₁ >0 or by increasing ρ"'₂ by -C_(x) e_(x1) /2 if e_(x1) <0

This adjustment e_(x1) =0 does not apply to e_(z) =0 already performed but produces a new variation of the zero by: ##EQU28##

Whatever it may be, the new value of the zero is measured and then set at the desired value by conventional functional adjustment of a principal resistor (θ=0) having a suitable parity determined by the sign of the zero.

As will be readily understood, all the calculations mentioned in the foregoing can be carried out by means of a computer which thus computes automatically the corrections to be applied to the gages. 

What is claimed is:
 1. A method for adjusting a resistance-gage force transducer (resistance gages R₁, R₂, R₃, R₄) comprising a resilient bar (1) attached at one end to a stationary support (2) and subjected at the other end to the force (P) to be measured, said bar (1) being adapted to carry resistance gages (R₁, . . . R₄) electrically connected to each other so as to form a measuring bridge for delivering an electrical signal which is a function of the force applied to said other end of the bar, said transducer being adjustable by means of said method in such a manner as to ensure that said electrical signal is proportional to the applied force and insensitive to the torsional and flexural couples generated by the displacements of the point of application of the force (P) to be measured, said method being distinguished by the following steps:A. Determination of the initial characteristics of the transducer, B. Computation of the relative errors of the transducer arising from a displacement of the applied force (P) as a function of the angle θ formed between the resistance gages (R₁, . . . R₄) and the longitudinal direction (O_(x)) of the bar, C. Cancellation of these errors by making modifications in one or a number of resistance gages in order to produce a modification of the angle θ aforesaid.
 2. A method according to claim 1, wherein the errors of the transducer are computed by means of the following relations:

    e.sub.x =e.sub.x.sbsb.o +1/C.sub.x  Σ cos 2θ

    e.sub.z =e.sub.z.sbsb.o +1/C.sub.z  Σ sin 2θ

where e_(x) and e_(z) are the errors due to a displacement of the force (P) applied respectively along the axis (O_(x)) of the bar (1) and along an axis (O_(z)) perpendicular to said bar axis and to the applied force (P), e_(x).sbsb.o and e_(z).sbsb.o are the initial errors determined during the step which involves initial characterization of the transducer, C_(x) and C_(z) are known constants which are established by design and by the conditions of initial characterization of the transducer,and wherein the corrections to be made in the angle θ of each resistor are determined from the relations given above in order to cancel the errors e_(x) and e_(z).
 3. A method according to claim 2 in which the resistance gages form a zero angle θ with the axis O_(x) of the bar, wherein the error e_(x) aforesaid is cancelled by applying to a resistance gage having a suitable parity a correction:

    dθ.sub.x ≅(C.sub.x |e.sub.x0 |/4)1/2

and by applying a correction -dθ_(x) to the other gage having the same parity and the error e_(z) is cancelled by applying to a gage having a suitable parity a correction:

    dθ.sub.z ≅C.sub.z |e.sub.z0 |/4

and by applying a correction -dθ_(z) to a gage having a different parity.
 4. A method according to claim 2 in which the resistance gages comprise groups such that in each group having a same parity there is a gage forming an angle θ=0 and a gage forming an angle θ=π/4, wherein the error e_(x) is cancelled by applying to one of the gages θ=π/4 a correction:

    dθ.sub.x =C.sub.x e.sub.x O/2

and the error e_(z) is cancelled by applying to a gage θ=0 a correction:

    dθ.sub.z =C.sub.z e.sub.z1 /2.


5. A method according to claim 3 in which the resistance gages (R₁ . . . R₄) are constituted by resistive layers having the shape of rectangles and applied on the bar (1), wherein the angle θ of the resistance gages is corrected by cutting two parallel grooves (l₁, l₂) in said layers so as to form a parallelogram with the two opposite sides of the rectangle formed by each gage, said grooves being inclined with respect to the initial direction of said gages at the angle dθ_(x) or dθ_(z) determined by the relations given above.
 6. A method according to claim 3 in which the resistance gages (R₁, . . . R₄) are constituted by resistive layers having the shape of rectangles and applied on the bar (1), wherein the angle θ of said resistance gages is corrected by forming notches (e₁, e₂, . . . ) transversely in the longitudinal edges of said gages in order to ensure that the resultant electrical direction (L₁) of said gages forms the angle dθ_(x) or dθ_(z) with the initial direction, said angle being determined by the relations given above.
 7. A method according to claim 6, wherein said grooves (l₁, l₂) or notches (e₁, e₂, . . . ) are cut by means of a laser beam.
 8. A method according to claim 3 in which the resistance gages are formed by a principal resistor (R₀) which makes a predetermined angle with the longitudinal axis (O_(x)) of the bar (1), each principal resistor (R₀) being connected in series with an additional resistor (R_(a), R_(b)) having a low ohmic value in comparison with the ohmic value of the principal resistor (R₀) and inclined at a predetermined angle θ with respect to said principal resistor, wherein the errors (e_(x)) and (e_(z)) are cancelled by modifying the ohmic value of one or a number of said additional resistors (R_(a), R_(b)), the effect of said modification being to modify the virtual angle made between the resistance gage and the axis (O_(x)) of the bar (1).
 9. A resistance-gage force transducer (resistance gages R₁, . . . R₄) comprising a resilient bar (1) such that one end of said bar is intended to be attached to a stationary support (2) and the other end is subjected to the force (P) to be measured, said bar (1) being adapted to carry resistance gages (R₁, . . . R₄) electrically connected to each other so as to form a measuring bridge for delivering an electrical signal which is a function of the force (P) applied to said other end of the bar, said transducer being so adjusted as to ensure that the signal is proportional to the applied force (P) and insensitive to the torsional and flexural couples generated by the displacements of the point of application of the force to be measured, wherein the angle θ formed between one or a plurality of resistance gages (R₁, . . . R₄) and the longitudinal direction (O_(x)) of the bar (1) satisfies the following relations:

    e.sub.x =e.sub.x.sbsb.o +1/C.sub.x  Σ cos 2θ=0

    e.sub.z =e.sub.z.sbsb.o +1/C.sub.z  Σ sin 2θ=0

where e_(x) and e_(z) are the errors due to a displacement of the force (P) applied respectively along the axis (O_(x)) of the bar (1) and along an axis (O_(z)) perpendicular to said axis of the bar and to the applied force, e_(x).sbsb.o and e_(z).sbsb.o are the initial errors determined during a step which involves initial characterization of the transducer, C_(x) and C_(z) are known constants established by design and by the conditions of said initial characterization.
 10. A force transducer according to claim 9 in which the resistance gages (R₁, . . . R₄) are constituted by resistive layers having the shape of rectangles and applied on the bar (1), wherein the resistance gages (R₁, . . . R₄) each have two parallel grooves (l₁, l₂) cut so as to form a parallelogram with the two opposite sides of the rectangle formed by each gage, said grooves being inclined with respect to the initial direction of said gages at an angle dθ_(x) or dθ_(z) which is determined by the following relations:

    dθ.sub.x ≅(C.sub.x |e.sub.x0 |/4)1/2

    dθ.sub.z ≅C.sub.z |e.sub.z0 |/4.


11. A force transducer according to claim 9, wherein each resistance gage comprises a principal resistor (R₀) which makes a predetermined angle with the longitudinal axis (O_(x)) of the bar (1), each principal resistor (R₀) being connected in series with additional resistors (R_(a), R_(b), . . . ) having a low ohmic value in comparison with the ohmic value of the principal resistor (R₀) and inclined at a predetermined angle θ with respect to said principal resistor, and wherein the ohmic value of one or a number of said additional resistors has been modified, the effect of said modification being to modify the virtual angle made between the resistance gage and the axis (O_(x)) of the bar (1). 